Problem: $h(n) = -5n^{2}-n$ $g(x) = 6x^{2}+6x+2(h(x))$ $ h(g(2)) = {?} $
Solution: First, let's solve for the value of the inner function, $g(2)$ . Then we'll know what to plug into the outer function. $g(2) = 6(2^{2})+(6)(2)+2(h(2))$ To solve for the value of $g$ , we need to solve for the value of $h(2)$ $h(2) = -5(2^{2})-2$ $h(2) = -22$ That means $g(2) = 6(2^{2})+(6)(2)+(2)(-22)$ $g(2) = -8$ Now we know that $g(2) = -8$ . Let's solve for $h(g(2))$ , which is $h(-8)$ $h(-8) = -5(-8)^{2}-(-8)$ $h(-8) = -312$